Let's just say that with 2 Karmapas....one gets 2 mirrors: to doubly reflect on our own selves and doubly increase practice.
We certainly ought to avoid hostility, which is only damaging to the Kagyu lineage as a whole. But there is no reason to accept two Karmapas. Take this guy Dawa Sangpo, an obvious charlatan, or any fake guru claiming to be Karmapa. They are not Karmapa, and no sensible person would say they are Karmapa.
Similarly, though Thinley Thaye Dorje and Orgyen Thinley Dorje both have far more convincing grounds for saying they are Karmapa than Dawa Sangpo, one of them is not
It is not even right to pretend
they are both Karmapas as an expedient to Buddhahood. As Shantideva says at 6.116-117,
Since they are both means of winning buddhahood
We say that beings are the same as buddhas
Even though they are not equal
In the boundless ocean of buddhas' qualities.
Yet even if a tiny fraction of those qualities
Were found contained in a certain being's heart
The three worlds made in offerings to them
Would not be enough to honour them.
So I say one is Karmapa, one is not. Perhaps I do not even know which one it is, though I think if one looks in an honest and straightforward way, one can easily see. But there is no reason for hostility on any side.
However, sometimes the truth is difficult to accept, so it is inevitable that sometimes, when one tries to uphold the truth, people will get upset. The thing to do is not to rub it in their faces if they're not ready for the truth. I would avoid doing that, but I would never say there are two Karmapas, which would be a deception.